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Questions tagged [shadow-tomography]

The study of solutions to the following problem: given an unknown D-dimensional quantum mixed state ρ, as well as known two-outcome measurements E1,...,EM, estimate the probability that Ei accepts ρ, to within additive error ε, for each of the M measurements. How many copies of ρ are needed to achieve this, with high probability?

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7 votes
2 answers
1k views

Are classical shadows useful?

according to the paper https://doi.org/10.1038/s42254-022-00535-2 , the advantage of classical shadows is doing measurements first and asking questions later. But in real experiments, who would do ...
yuanyi_thu's user avatar
2 votes
1 answer
100 views

Is there a tight operator frame that is also a POVM?

We define the tight operator frame as a set of operators $\{E_i\}_{i=1}^{n}$ satisfying \begin{equation} \sum_{i=1}^n \vert \langle \langle E_i \vert X \rangle \rangle \vert^2 = C \Vert V \Vert_2^2, \...
Michael.Andy's user avatar
0 votes
1 answer
49 views

Inverse channel of the Pauli 4 POVM

I'm currently grappling with a challenge in comprehending the inverse channel of the Pauli 4 POVM. The POVM elements are defined as follows: $ M_0 = \frac{1}{3} |0\rangle\langle0|, \quad M_1 = \frac{1}...
Yuval Idan's user avatar
2 votes
0 answers
103 views

What is the mistake in this Qutip implementation of the classical shadows protocol (Huang et. al. 2020)?

So I'm trying to replicate the results from Huang's paper, following Pennylane's tutorial. But instead of using Pennylane (in particular their recently implemented ClassicalShadow class), I'm trying ...
EdwardGHPhy's user avatar
3 votes
1 answer
294 views

How are classical shadows stored efficiently?

The paper states that classical shadows can be stored efficiently by stabilizer formalism. But I'm confused what information is stored? I can't tell the efficiency come from. In the paper,the ...
LinZaisheng's user avatar
1 vote
1 answer
363 views

State tomography with Pauli basis measurements for a high number of qubits

My end goal is to recover the quantum state in its computational basis or reduced density matrix of a high number qubit circuit in a real QPU. Taking into account that the number of qubits will be ...
Borja Aizpurua's user avatar
8 votes
1 answer
517 views

Using Classical Shadow to predict quantum state's fidelity has nothing to do with the dimension of the density matrix?

Using classical shadow(or refer to this post for basic things about classical shadow), we can predict linear functions like $Tr(O\hat{\rho})$ with number of copies(referred paper): $$ 2\log(2M/\delta)*...
narip's user avatar
  • 2,989
3 votes
1 answer
514 views

How do I pick a random Clifford operation in Stim?

I want to sample random n-qubit Clifford operations. How do I do that in Stim? (Self-answering because this was requested when the feature already existed)
Craig Gidney's user avatar
  • 37.8k
6 votes
1 answer
860 views

Implement the classical shadow coding error?

I'm trying to reproduce the basic method of classical shadow, which is based on the tutorial of pennylane. However, I've met some realization problems here when I finish reading the tutorial of ...
narip's user avatar
  • 2,989
9 votes
2 answers
603 views

Why is the complexity of $n$-qubit state tomography not upper bounded as $O(3^n)$?

Consider the task of fully determining an $n$-qubit state $\rho$ which can be written as \begin{equation}\tag{1} \rho = \sum_{p \in \{I, X, Y, Z\}^n} \text{Tr}(\rho P_{p}) P_{p} \end{equation} and ...
forky40's user avatar
  • 7,123
5 votes
2 answers
1k views

Inverting the depolarizing channel

I have a depolarizing channel acting on $2^n \times 2^n$ Hermitian matrices, defined as $$\tag{1} \mathcal{D}_p (X) = p X + (1-p) \frac{\text{Tr}(X)}{2^n} \mathbb{I}_{2^n} $$ where $\mathbb{I}_{d}$ is ...
forky40's user avatar
  • 7,123
11 votes
2 answers
755 views

In shadow tomography, how is the state reconstructed from its shadows?

I'm reading Huang et al. (2020) (nature physics), where the authors present a version of Aaronson's shadow tomography scheme as follows (see page 11 in the arXiv version): We want to estimate a state $...
glS's user avatar
  • 25.4k